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Rational points on twists of X-0(63)

Autor
Bruin, N.; Fernandez, J.; Gonzalez, J.; Lario, J.-C.
Tipus d'activitat
Article en revista
Revista
Acta arithmetica
Data de publicació
2007-04
Volum
126
Número
4
Pàgina inicial
361
Pàgina final
385
DOI
https://doi.org/10.4064/aa126-4-6 Obrir en finestra nova
Projecte finançador
Curvas de Shimura, Superficies Abelianas y Thetanullwerte
Repositori
http://hdl.handle.net/2117/474 Obrir en finestra nova
URL
https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/acta-arithmetica/all/126/4/82724/rational-points-on-twists-of-x-0-63 Obrir en finestra nova
Resum
Let $\varrho\colon G_\mathbb{Q}\longrightarrow PGL_2(\mathbb{F}_p)$ be a Galois representation with cyclotomic determinant, and let $N>1$ be an integer that is square mod $p$. There exist two twisted modular curves $X^+(N,p)_\varrho$ and $X^+(N,p)'_\varrho$\, defined over~$\mathbb{Q}$ whose rational points classify the quadratic $\mathbb{Q}$-curves of degree $N$ realizing $\varrho$. The paper focuses on the only genus-three instance: the case $N\!=7,\,p=3$. From an explicit description of the au...
Paraules clau
Chabauty Methods, Elliptic Curves, Galois Representations, Genus-three Curves, Prym Varieties, Quadratic Q-curves
Grup de recerca
TN - Grup de Recerca en Teoria de Nombres

Participants

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